You still qualify to apply for "VAWA."As a battered spouse of USC, you can file an immigrant visa petition without your spouse's signture/knowledge. This allows victims to seek both safety and independence from their abuser, who is not notified about the filing.
Consult with an atttorney. I wish you luck.
I agree with my colleague. Please review 2013 HHS Poverty Guideline Affidavit of Support. You must add the number of household plus 1 (for your mother) for the sponsor's household size. Anyone with USC or LPR status can sponsor.
Do your best to prove bona fide marriage. I think there is no such thing as "overkill" when it comes to proving good faith marriage. You definitely must file marriage certificate and child's birth certificate.
You are dealing with two sets of law here: family and immigration. Family law will help you deal with your kid's custody issue. Talk with a family law attorney in Houston Texas.
Immigration law: I want to advise you to talk with an immigration attorney about U visa to sort out your immigration status. You will need to report the domestic violence to a law enforcement officer.
Get help please. There are many non-profit organizations/shelters you can reach out. Good luck.